Figure 2.3: Histograms of overconfidence measures (i) to (v)
Table 2.4: Correlation table of our five measures of overconfidence and quiz perfor-mance
Overestimation Overplacement
(i) (ii) (iii) (iv) (v)
(i) 1
(ii) 0.77*** 1
(iii) 0.26*** 0.22*** 1
(iv) 0.41*** 0.44*** 0.46*** 1
(v) 0.36*** 0.38*** 0.44*** 0.90*** 1
Quiz performance -0.14* -0.19*** -0.25*** -0.68*** -0.68***
Notes: N=190. Significance of the Spearman-rank test at the 1, 5, and 10 percent level is denoted by ***, **, and *, respectively.
Table 2.5: Measures of absolute and relative overconfidence
Measure Level of overconfidence
(i) Degenerate = self-assessment - quiz performance (QP) (ii) Token
distribution task
=
20
P
i=0
ti·i/20−QP , where ti is the amount of points for category i
(iii) Median =
1 if worse than median although indicated better 0 if median comparison is correct
−1 if better than median although indicated worse (iv) Upward
distribution
= amount of subjects that are better - self-assessment
(iv) Downward distribution
= self-assessment - amount of subjects that are worse
Appendix 2.B
Instructions, translated into English. General instructions and instructions for first, second, and fourth part of the experiment were identical across treatments. Instruc-tions for the third part of the experiment differed across treatments.
GENERAL INSTRUCTIONS
You are taking part in a decision-making experiment in which you have the oppor-tunity to earn money. The amount of money you earn is paid to you upon completion of the experiment. Please read the instructions carefully. The instructions are iden-tical for all participants. If you have any questions, please raise your hand. The experimenter will answer your question at your place. During the experiment, you have to remain silent. Violation of this rule leads to immediate exclusion from the experiment and all payments.
All monetary units in the experiment are measured in points, and 100 points = 1 Euro.
This experiment consists of four parts. In all parts, you can earn money. Your payoff from the experiment results from the sum of your payoffs in all parts. In the following we will go through the instructions for the first part of the experiment.
After the first part is completed, we will provide you with the instructions of the second part.
INSTRUCTIONS FOR THE FIRST PART OF THE EXPERIMENT
In the first part of the experiment you will be asked 20 quiz questions. You will always be offered 4 possible answers of which exactly one will be correct. Please always select one of the four possible answers. You get 20 points for each correct answer. After you have answered the first 10 questions, please click on the OK button. Then a new screen with 10 more questions will appear. Please confirm your
responses again with the OK button.
Do you have any questions?
INSTRUCTIONS FOR THE SECOND PART OF THE EXPERIMENT (Only on screen)
We will ask you five questions concerning your estimation of your quiz perfor-mance. The questions are on the screen and will not be read together. The questions are identical for all participants. For each question, you can again earn points. The points will be added to the points earned in the quiz. Please give your answers on the screen and confirm them with the OK button. If you have any questions, please raise your hand, we come to your place.
Question 1: Please estimate now as good as possible the number of your correct quiz answers.
Your payment will look like this: You earn 200 points if your estimate is correct and 50 points, if your estimate is a number next to the correct number.
Question 2: Please estimate now again as good as possible the number of your correct quiz answers.
This time you do not have to commit to a number. Instead, you get 100 points which you can allocate into any of 21 fields. Each field of 0-20 is the number of correct answers. Your payment is as follows: The number of points that you have allocated to the field that corresponds to your correct number of quiz answers will be doubled and paid. The points, on a field next to the correct field, will be paid to 50%. For example, participant xy has 10 correct answers and distributes the coins as follows:
Correct quiz questions ... 9 10 11 12 13
Token 0 10 50 40 0 0
then the participant gets: 0.5·10 + 2·50 + 0.5·40 = 125 points.
Please enter a ”0” in any field, where you do not want to allocate points to.
12 quiz performances in the room?
For a correct estimate you will get 100 points.
Question 4: What do you think, how many of the other 23 participants answered more quiz questions correct than you?
You earn 200 points if you have guessed correctly and 50 points, if your estimated number is one number next to the correct number.
Question 5: What do you think, how many of the other 23 participants have less correct quiz answers than you?
You earn 200 points if you have guessed correctly and 50 points, if your estimated number is one number next to the correct number.
If you have any questions, please raise your hand.
INSTRUCTIONS FOR THE THIRD PART OF THE EXPERIMENT
In part 3 you will be randomly assigned to another participant of the experiment.
You will learn at no time of the experiment the identity of the assigned participant.
You decide in part 3, if you want to participate in a competition against your ran-domly matched participant or not.
If you do not want to participate, you will get 200 points, whatever decision your opponent takes.
If you want to participate, you will produce an individual output. The output corresponds to your number of correct answers in the quiz. You compete against your randomly assigned opponent with your output.
Output = number of correct quiz answers
Example: Player xy has solved 1 of 20 questions in the quiz correctly. If player
xy participates, he or she produces an output of 1.
If you participate, your payoff depends on your own output and the output of your opponent in case he or she participates, too. The rules of the competition are as follows:
1. If you participate but your opponent does not, you win automatically.
2. If you and your opponent participate, you win if you have a higher output than your opponent. But if you have a lower output than your opponent, you lose.
3. If you and your opponent participate and you both have the same output, the computer randomly decides who wins and who loses.
The winner receives 400 points and the loser gets 100 points. You will find the payoff matrix below on all of your decision screens.
Participation No participation
Winner prize 400 200
Loser prize 100 200
DECISION
The only thing you need to do is to decide for or against participation in the competi-tion. You make your decision on the screen and confirm it with the button “Confirm decision”.
CONTROL QUESTIONS
Before part 3 starts, we ask you a few control questions to ensure that all participants understand part 3 of the experiment. You earn no money for correct answers of the control questions, nor do we take money away from you for a wrong answer. However, part 3 starts only when all participants have answered all control questions correctly.
Example: Player 1 solved 10 questions correct and player 2 solved 8 questions correct.
Question 2: How many points does player 1 receive if he does not enter the competition?
Question 3: What is the output of player 2 if he enters the competition?
Question 4: How many points does player 3 receive if he does not enter the competition?
Question 5: Who wins the competition if both enter?
Question 6: How many points does player 1 get if both enter the competition?
Question 7: How many points does player 2 get if both enter the competition?
Question 8: How many points does player 1 get if only he enters the competition?
Question 9: How many points does player 2 get if only he enters the competition?
Any questions?
We present now the additional instructions four each treatment. Note that each subject participated only in one treatment.
Treatment No Info You will be randomly assigned to one participant. You both make your decision to participate in the competition. You receive no information about the participant that is randomly matched to you and likewise your randomly matched participant does not receive any information about you before you both make your decision about participation in the competition. Your decision screen looks like this:
Please confirm your decisions by pressing the button ”Confirm decision ”. Any questions?
Treatment Distribution You will be randomly assigned to one participant. You both make your decision to participate in the competition. Before that, you get sum-marized information on all participants in the room, including you. All participants receive this information on the screen. On the screen, you will see a table with the number of correctly solved quiz questions from 0-20 and the number of participants that solved the corresponding number of quiz questions correctly.
Example: 12 participants answered all questions wrong, and the remaining 12 participants answered all questions correct. Your screen would look like this:
Please confirm your decisions by pressing the button ”Confirm decision”. Any questions?
Treatment TrueYou will be randomly assigned to one participant. You both make your decision to participate in the competition. Before that, you receive the informa-tion how many quiz quesinforma-tions your randomly matched participant answered correctly.
This information is shown on your decision screen. Likewise, your randomly matched participant will be informed about your number of correctly solved quiz questions.
Then both of you take the decision to participate. Your decision screen looks like this with the respective number of correct quiz answers of your matched participant :
Please confirm your decisions by pressing the button ”Confirm decision ”. Any questions?
Treatment True & Belief You will be randomly assigned to one participant. You both make your decision to participate in the competition. Before that, you receive two pieces of information about your randomly matched participant.
1. how many questions he/she has correctly answered in the quiz
2. how many questions he/she estimated that he/she answered correctly.
This information is shown on your decision screen. Likewise, your randomly matched participant will be informed about your number and estimation of your correctly solved quiz questions. Then both of you take the decision to participate. Your deci-sion screen looks like this with the respective number and estimation of correct quiz
answers of your matched participant :
Please confirm your decisions by pressing the button ”Confirm decision”. Any questions?
INSTRUCTIONS FOR THE FOURTH PART OF THE EXPERIMENT
In the fourth part of the experiment, you make 30 decisions. You have to choose 30 times between Option A and Option B. Under Option A, you will receive a secure payment that starts with 0 points in the first decision round and increases to 400 points in the last decision round. Under Option B you will receive a lottery. In the lottery, you get with 50% probability either 100 points or 400 points. The lottery is in all 30 decisions the same.
We pay one of the 30 decisions, which is chosen randomly. You confirm your 30
decisions with the OK button. Do you have any questions?
Chapter 3
Auctions with Loss Averse Bidders
3.1 Introduction
Since Kahneman and Tversky (1979), loss aversion and reference dependent prefer-ences have been applied to a variety of empirical and theoretical economic problems.
When applying models of loss aversion, the modeller is required to decide over what individuals have feelings of gains and losses. This is the problem of narrow versus wide bracketing. To illustrate the problem, consider the series of experiments con-ducted by Kahneman, Knetsch, and Thaler (1990), who study the endowment effect in competitive markets. When subjects are given actual goods, the endowment effect has an impact on trading volumes; if, however, subjects are endowed with money rather than a good, they observe no endowment effect. The explanation given is that when trading money for coffee mugs, there is a friction caused by a loss in one and a gain in the other dimension. When money is traded for money, this friction disappears. K¨oszegi and Rabin (2006) propose a model which rationalizes the experi-mental findings mentioned, using the concept of consumption dimensions, over which individuals have gain loss utility in an additively separable manner. Applying the model of K¨oszegi and Rabin (2006, 2007), we derive the equilibrium bidding behavior in the first price auction (FPA) and in the all pay auction (APA) for general environ-ments with independent private values (IPV). In addition, we study the behavioral implications of loss aversion on bidding strategies, and compare the revenue across auction formats. In one specification, we consider gains and losses in two dimensions
separately, about whether they receive the object or not, and how much they pay.
In the other specification, we consider gains and losses over the entire risk neutral payoff, i.e. the valuation less the bid. The first specification represents narrow brack-eting, while the second one represents wide bracketing. With one dimension, we show that the expected revenue for the auctioneer is higher in the FPA than in the APA, and with two dimensions, we show that the opposite is true for the revenue ranking between the FPA and the all pay auction.
In order to test the theoretical predictions, we conduct laboratory experiments, in which either money or a real object is auctioned in both a FPA and an APA. We find that in both settings, the average revenue is significantly higher in the first price auction, suggesting that bidders may behave according to the one dimensional model, although a real object is auctioned. Whereas our findings are inconsistent with the two dimensional model, they are consistent with the one dimensional model.
The paper contributes to the literature on loss aversion and reference depen-dent preferences in several ways. Comparing our results to the ones in Kahneman, Knetsch, and Thaler (1990), we conclude that whether individuals do a narrow or a wide form bracketing of gains and losses depends on the environment under consider-ation. While competitive markets and auctions are similar in many ways, the degree of uncertainty is a lot higher in auctions. Additionally, we provide an estimate for the ratio of marginal disutility of losses to marginal utility of gains of 1.42, using the gen-eralized method of moments for the data obtained in the induced value experiments.
Furthermore, we show that when applying the K¨oszegi and Rabin (2007) model, the theoretical predictions depend crucially on the modeller’s decision how to define the consumption dimensions over which individuals experience gains and losses.
Finally, our experimental data shows that there is no measurable difference be-tween auctioning an actual good or simply money in auctions with induced valuation.
This result is important from a methodological view for experimenters that choose to conduct auction experiments in the laboratory or in the field.
3.1.1 Related Literature
Auction Theory and Risk Preferences
Riley and Samuelson (1981), Maskin and Riley (1984), Matthews (1987), and Fibich, Gavious, and Sela (2006) study the implications of risk averse bidders in auction settings. Lange and Ratan (2010) consider the case of loss averse bidders for the FPA and the Vickrey auction and show that the FPA yields higher expected revenue than the Vickrey auction, independent of whether bidders consider gambles in one or two dimensions. Shunda (2010) shows that under a different notion of reference dependence, the auctioneer can increase his expected revenue by introducing a buy now price. In the present paper, we focus on a specific class of hybrid auctions, incor-porating both the FPA and the APA, and study the bidders’ behavior and revenue (non) equivalence across different auction formats. Furthermore, while the revenue ranking of the FPA and the Vickrey auction in both models is the same (Lange and Ratan (2010)), our analysis provides another testable implication of reference depen-dence with revenue data alone. Using a general mechanism design approach in the spirit of Myerson (1981), Eisenhuth (2012) shows that in the one dimensional model, the FPA maximizes the expected revenue among all efficient auctions, and that in the two dimensional model, any optimal auction is fully all pay. In light of these results, we focus on the optimal auction (in the class of efficient auctions) in each case when considering the FPA and the APA.
Experimental Economics
The empirical literature on the APA is small, as it is not a commonly used auction format. To the best of our knowledge, Noussair and Silver (2006) provide the only empirical analysis comparing the APA and the FPA in a laboratory setting with in-dependent private values. They replicate the environment in Cox, Smith, and Walker (1982) and Cox, Roberson, and Smith (1988), who study the FPA, and compare the revenue data from these studies to their revenue data on the APA. Their finding is that the APA yields significantly higher revenue than the FPA. One confounding effect is that they provide subjects with an initial endowment of nearly seven times as much as Cox, Smith, and Walker (1982) and Cox, Roberson, and Smith (1988).
Thereby, Noussair and Silver (2006) lose some control over their data comparison Furthermore, they observe bids of 0 for the lowest types in either auction format.
Real object auctions are not studied. Lucking-Reiley (1999) studies real object field auctions using the FPA, the Vickrey auction, the English auction, and the Dutch auction with Magic cards and refutes revenue equivalence; an analysis of the APA is missing. Moreover, as the data are collected through online auctions, bidders do not know how many opponents they are facing in the auction. We contribute to the experimental literature by studying revenue equivalence between the APA and the FPA, explicitly differentiating between auctioning money and an actual object.